Multiple antennas employed at the transmitter and receiver can significantly increase the system capacity. By transmitting independent symbol streams in the same frequency bandwidth, usually referred to as spatial multiplexing (SM), achieves a linear increase in data rates with the increased number of antennas. On the other hand, by using space-time codes at the transmitter, reliability of the detected symbols can be improved by exploiting transmit diversity. Both schemes assume no channel knowledge at the transmitter.
However, in a practical wireless systems such as the 3GPP (3rd Generation Partnership Project) LTE (Long Term evolution), HSDPA (High Speed Downlink Packet Access), HSPA (High Speed Packet Access) and WiMAX (Worldwide Interoprability for Microwave Access) systems, the channel knowledge can be made available at the transmitter via feedback from the receiver to the transmitter. A MIMO (Multiple Input Multiple Output) transmitter can utilize this channel information to improve the system performance with the aid of precoding. In addition to beam forming gain, the use of precoding avoids the problem of ill-conditioned channel matrix.
In practice, complete CSI (channel state information) may be available for a communication system using TDD (time division duplex) scheme by exploiting channel reciprocity. However, for a FDD (frequency division duplex) system, complete CSI is more difficult to obtain. In a FDD system, some kind of CSI knowledge may be available at the transmitter via feedback from the receiver. These systems are called limited feedback systems. There are many implementations of limited feedback systems such as codebook based feedback and quantized channel feedback. 3GPP LTE, HSDPA and WiMAX recommend codebook based feedback CSI for precoding.
In a codebook based precoding, predefined codebook is defined both at transmitter and receiver. The entries of codebook can be constructed using different methods such as Grassmannian, Lyod algorithm, DFT matrix etc. The precoder matrix is often chosen to match the characteristics of the NR×NT MIMO channel matrix H (NR being the number of receive antennas and NT being the number of transmit antennas), resulting in a so called channel dependent precoding. This is also commonly referred to as closed-loop precoding and essentially strives for focusing the transmit energy into a signal subspace which is strong in the sense of conveying much of the transmitted energy to the UE (user equipment). The signal subspace in this context is a subspace of a signal space that is defined in any number of dimensions including space, time, frequency, code, etc.).
In addition, the precoder matrix may also be selected to strive for orthogonalizing the channel, meaning that after proper linear equalization at the UE, the inter-layer interference is reduced. At the receiver, it is common to find SINR (signal-to-interference-plus-noise ratio) with different codebook entries and choose the rank/precoding indicator (rank/precoding index) which gives the highest spectral efficiency (also referred to as channel capacity). In this context, rank indicates the number of data streams that can be simultaneously transmitted from a transmitter to a receiver.
The performance of a closed-sloop MIMO system generally improves with the cardinality (size) of the codebook set. At the receiver, RI (rank indicator or rank information) and PCI (precoding control indicator or precoding control index) are sent back to the transmitter every Tri (transmission time interval) or multiples of Tri (for example 5 in LTE, ⅓ in HSDPA). In general, finding the rank information and precoding control index is cumbersome and involves many computations. The complexity is huge in case of a closed-sloop MIMO when the codebook is large. For example, HSDPA/LTE defines a codebook for a 4-Tx antennas system with 64 codewords (16 codewords per rank). As the number of antennas increase, the complexity can increase exponentially. This makes it difficult to implement conventional methods of providing feedback to improve performance.